Determine whether the statement is true or false. Prove the statement directly f

Question

Determine whether the statement is true or false. Prove the statement directly from the definitions if it is true, and give a counterexample if it is false. 1.) The product of any two integers is a multiple of 4. 2.) A sufficient condition for an integer to be divisible by 8 is that it be divisible by 16. Determine whether the statement is true or false. Prove the statement directly from the definitions if it is true, and give a counterexample if it is false. 1.) The product of any two integers is a multiple of 4. 2.) A sufficient condition for an integer to be divisible by 8 is that it be divisible by 16. Determine whether the statement is true or false. Prove the statement directly from the definitions if it is true, and give a counterexample if it is false. 1.) The product of any two integers is a multiple of 4. 2.) A sufficient condition for an integer to be divisible by 8 is that it be divisible by 16.

Explanation / Answer

1) False: because lets consider 3 and 5, their product is 15 but it is not a mulltiple of 4.

2) True: It is a sufficient condition but not a necessary one

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